Manually operated fluid dispensers are known for dispensing hand cleaning fluid onto a person's hand. Such dispensers typically have a cover to enclose the operational mechanisms of the dispensers. Previously known dispensers suffer the disadvantage that covers for the dispensers are difficult for a user to move between open and closed positions and to remove the cover from the dispenser. To address this problem, U.S. Pat. No. 10,182,685 to Ophardt et al., issued Jan. 22, 2019, which is incorporated herein by reference, discloses a fluid dispenser in which a cover actuator member is provided for moving a cover between an open position and a closed position relative to a housing of the dispenser. The present inventors have appreciated that the dispenser as disclosed in U.S. Pat. No. 10,182,685 can be further improved.